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The Gemora states: An act of kindness or charity performed by an idolater is regarded as a sin. This is because they are only performing these good deeds to live longer, or that their reign should continue, or in order to glorify themselves, or to rebuke the Jews.
The Gemora in Sotah (47a) states: When there increased the number of Jews who accepted charity from idolaters, the idolaters were on top and Israel was on bottom.
Our Gemora says that when idolaters give tzedakah it serves as an atonement for them. Because it serves as an atonement, Rav Ami refused to accept tzedakah from Ifra Hurmiz. Even Rava only accepted it for the sake of peaceful relationship with the government, but otherwise, he would not have accepted it. This is based upon a verse which teaches us that the idolaters will become weak and broken once their charitable deeds have dried up, and therefore, we don’t give them opportunities for more merits. However, the Gemora says that if we were to use the funds to support non-Jewish causes (which Rashi explains that we support anyway for the sake of peaceful relationship with the government), it would not give them any special merit. It is only if we use the funds to support Jews that it is considered a merit for them.
Tosfos (8a d.h. yasiv) points out that the Gemora in Eruchin (6b) implies that we would accept donations to synagogues that come from idolaters. Why? Tosfos explains that donations to synagogues are considered like korbanos and we do accept korbanos from idolaters.
The Gemora (Nazir 62a) cites a Scriptural source to teach us that an idolater can vow vowed-offerings and freewill-offerings just like Jews.
The Haga’os Ashri (here) brings the following question in the name of the Maharich: Why are we not allowed to accept charity from an idolater, but we are permitted to accept his korbanos?
He answers in the name of his Rebbe: A voluntary korban is not brought to serve as atonement, and therefore, we are not concerned if they offer a sacrifice, for those do not bring about forgiveness and they will not serve as a protection for them. However, one who gives charity receives atonement for his sins, and merits protection for his good deed. It is not in our best interests to assist them in this matter.
What does the Haga’os Ashri mean that vowed-offerings and freewill-offerings are not meant for the purpose of atonement? What is accomplished for the idolaters aside from atonement? Furthermore, the Gemora says in Sukkah (55b) that the idolaters destroyed the Holy Temple, not realizing what they will be losing. When we had the Temple, the Altar served as an atonement for them, but now they have nothing to atone for them. The Gemora in Sukkah clearly implies that the purpose for their korbanos were to be an atonement, which contradicts the Haga’os Ashri?
The distinction of the Haga’os Ashri is found in the Shach and Taz (Y.D. 254:4) to explain the Rama who says that we do accept donations to synagogues from idolaters, but don’t accept tzedakah from them (unless the money was air-marked for tzedakah and must be accepted for the sake of peaceful relationship with the government).
Reb Avi Lebowitz suggests the following: Perhaps the Gemora in Sukkah is not referring to the vowed-offerings and freewill-offerings that the idolaters bring, rather the Holy Temple, in general, served as an atonement for the entire world, including the idolaters. But the vowed-offerings and freewill-offerings, and donations to synagogues that we accept from idolaters is because it allows them to have a share in our prayers, but it will not serve as an atonement to prevent them from being destroyed for sins that they have committed. Tzedakah to the poor which would serve as an atonement for sins that they have committed, we refuse to accept from them unless we have no choice (such as for the sake of peaceful relationship with the government).
The Chochmas Adam (146:3) explains this idea a bit further: Tzedakah to the poor is tantamount to a korban chatas which we do not accept from idolaters because we don’t give them opportunity for atonement, but freewill-offerings, we do accept from them, so we can also accept gifts to synagogues.
It would seem that this prohibition, which forbids accepting tzedakah from them, only applies to tzedakah to the poor, but donations to Yeshivos and donations for kindness activities which do not go to the poor, would be like vowed-offerings and freewill-offerings that we can accept from them. But perhaps when it comes to the studying of Torah, where the donation buys them a share in the Torah, we should not provide them with that opportunity either.